Bloch Domain Walls Research Articles

Phase-locked spatial domains and Bloch domain walls in type-II optical parametric oscillators.

We study the role of transverse spatial degrees of freedom in the dynamics of signal-idler phase locked states in type-II optical parametric oscillators. Phase locking stems from signal-idler polarization coupling which arises if the cavity birefringence and/or dichroism is not matched to the nonlinear crystal birefringence. Spontaneous Bloch domain wall formation is observed numerically and the dynamics and chiral properties of the fronts are investigated. Bloch walls connect homogeneous regions of self-phase-locked solutions by means of a polarization transformation. The parameter range for phase locking is found analytically. The polarization properties and the dynamics of walls in one and two transverse spatial dimensions are explained. The transition from Bloch to Ising walls is characterized, the control parameter being the linear coupling strength. The wall dynamics governs spatiotemporal dynamical states of the system, which include transient curvature driven domain growth, persistent dynamics dominated by spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising walls.

Influence of geometry on domain wall propagation in a mesoscopic wire

The propagation of a single magnetic Bloch domain wall (DW) in a mesoscopic wire is studied by use of the extraordinary Hall effect. Whereas a straight DW propagates freely in a wire with constant lateral width, the propagation in a Hall cross reveals that both DW shape and DW velocity vary strongly as a function of DW position. These results give the first experimental evidence that the dynamical properties of a magnetic DW in a patterned structure are strongly affected by the device geometry. This has to be taken into account for future applications to spin electronic devices.

Influence of magnetic domain-wall width and shape on magnetoresistance measurements

The influence of magnetic domain walls (DWs) on magnetoresistance in various exchange-bias ferrimagnetic/(ferrimagnetic or ferromagnetic) bilayer systems (Gd68Fe32/Tb55Fe45 and Fe60Gd40/Fe55Sn45) is presented. These systems allow one to create well-defined DWs of various size and shape. The DW morphology is controlled by the applied magnetic field in the film plane. By changing the amplitude of the field, the DW thickness can be controlled, whereas the rotation of the field in plane allows one to create a θ° Bloch DW (90° DW, 180° DW,…). The electrical resistivity of the sample was measured relative to the applied magnetic field (amplitude and direction). The influence of the shape and size of the DW on magnetoresistance was followed. For the two amorphous samples, it made it possible to fit the variation of resistivity relative to the DW thickness and shape using a model based on anisotropic magnetoresistance.

Magnetic field dependence of the Gilinsky mode of the domain wall spectrum in a uniaxial ferromagnet

The dependences of the translation mode and the Gilinsky mode of the domain wall spectrum on the value of an external magnetic field directed along the plane of the Bloch domain wall and perpendicular to the axis of anisotropy are determined. The diagram of stability of the domain wall polarity in a magnetic field is calculated. The behavior of the modes in the vicinity of the point of reorientation of the domain wall polarity is analyzed.

Domain wall in ultrathin magnetic film: Internal structure and dynamics

Detailed micromagnetic study of internal structure and dynamics of domain wall in ultrathin magnetic film with thickness tf≪lex (lex is the exchange length) is carried out. It is revealed that deviations of stationary magnetization distribution inside the wall from the one of the Bloch domain wall are small and proportional to (tf/lex)Q−1. The limiting velocity of uniform domain wall motion coincides with the same for the Bloch wall (Walker’s critical velocity) with an accuracy of terms proportional to (tf/lex)2. It is also found that the same small parameter describes deviation of stationary distribution of magnetization in a vertical Bloch line and deviation of Bloch line velocity from the expressions found for films with tf>lex.

Bloch domain walls in type II optical parametric oscillators

Evidence of Bloch domain walls in nonlinear optical systems is given. These walls are found in the transverse fields of optical parametric oscillators when the polarization degree of freedom, the cavity birefringence, and (or) dichroism are taken into account. These domain walls arise spontaneously and exhibit defects where Bloch walls of different chirality join together. Two dynamic regimes are found:In the first one the vector field approaches a final homogeneous state, and in the other the walls are continually generated and annihilated. This dynamic behavior is caused by the fact that walls of opposite chirality move spontaneously with opposite velocity.

3-D micromagnetic simulation of a Bloch line between C-sections of a 180° domain wall in a {1 0 0} iron film

The micromagnetic structure and energy of a Bloch line (BL) in an asymmetric 180° Bloch domain wall in a 60 nm {1 0 0} iron film have been calculated. In the wall cross-sections on either side of the BL, the flux of magnetisation transverse to that of the domains was ‘C’ shaped, roughly normal to the plane of the film in its interior but bending nearly parallel to the surfaces as they are approached. The sense of this transverse flux is reversed at the BL. The energy of this BL was calculated to be considerably lower than the energies reported earlier for BLs in walls having ‘S’ shaped transverse flux cross-sections.

Observation of a well characterized 180° domain wall by polarized neutron reflectometry

In a GdFe (500 Å)/TbFe(50 Å) amorphous sample, a 180° magnetic domain wall (DW) can be created in the soft GdFe magnetic layer and be pinned by the hard TbFe layer. The modulation vector of the Bloch DW is perpendicular to the film plane and the magnetization lays in plane. Using different amplitude of the applied magnetic field, we can control the width of the DW at the interface between GdFe and TbFe. The polarized neutron reflectivity measurements in the presence of a DW exhibits a clear discrepancy with the reflectivity measured in the saturated state. The influence of the DW thickness is observed. These results are confirmed by simulation.

Magnetic and morphological properties of ultrathin Fe layers in Zr/Fe/Zr trilayer structures

The structural and magnetic properties of Zr/Fe/Zr trilayer structures, composed of ultrathin layers of Fe stacked between two pure Zr layers, have been studied by means of X-ray diffraction (XRD), conversion electron Mössbauer spectroscopy (CEMS) and magnetometry techniques. The XRD results, as well as the room temperature saturation magnetization, show a decrease in the amount of bcc-Fe on decreasing the Fe layer thickness. The thickness dependence of the room temperature coercivity is interpreted as giving evidence for a switch from a Bloch domain wall structure to a Néel interacting cluster behaviour, as the Fe layer thickness is decreased below 16nm. Below this thickness, the temperature dependence of the coercivity as well as the thermomagnetization behaviour, suggest a magnetic structure composed of crystalline bcc-Fe interacting clusters. This effect can be related to the appearance of an amorphous Fe–Zr alloy phase at the grain boundaries which affects progressively the magnetization process as the magnetic layer thickness is reduced.

Microwave excitations of a domain wall in a cubic magnet with induced anisotropy

Theoretical and experimental studies are made of the spectra of spin wave excitations localized at a Bloch domain wall in a ferromagnet with combined cubic and biaxial anisotropy in [100]-or [110]-oriented bismuth-containing iron garnet films. This analysis of the spectra is used as the basis to calculate diagrams of stable states of a homogeneous Bloch domain wall as a function of the magnetic parameters in these materials. Results of measurements of the oscillation spectrum of an isolated domain wall in the mega-and gigahertz frequency ranges are presented. A description is given of an effect where the spin-wave excitations of the Goldstone translational branch and the high-frequency Gilinskii unidirectional mode are hybridized.

Exchange-spring systems: Coupling of hard and soft ferromagnets as measured by magnetization and Brillouin light scattering (invited)

An experimental and theoretical study is presented of the normal magnetic modes in spiral ferromagnetic structures. The bilayer system studied consists of Fe layers (25, 50, 100, and 200 Å thick) that are exchange coupled to 200 Å thick SmCo films that have ≈200 kOe anisotropies. The Fe spiral—induced by an external magnetic field that is applied opposite to the direction of the magnetized film—results in a structure similar to that encountered in a Bloch domain wall. The magnetization and the field dependence of the magnons in various Fe films are explained by the theoretical model.

Visualization of Bloch waves and domain walls

The theory of wave propagation in periodic structures1 and its major concept, Bloch's theorem, have typically been assigned to the realm of solid-state physics2, but they are now becoming useful in optics3, acoustics4 and hydrodynamics5. Bloch's theorem is constructive and aesthetic, starting from the idea of perfect order and dealing with infinite extended states. But Bloch's solution is unstable against a small amount of disorder.

A micromagnetic model domain wall resonance in thin films

Domain wall and ferromagnetic resonances in perpendicularly magnetised ferromagnetic thin films are studied using a numerical time dynamic micromagnetic method. The dynamic response of Bloch domain walls in stripe domain patterns is examined for different orientations of a static applied field. The calculations are in good agreement with recent experimental results.

Effect of magnetic anisotropy on the mobility of the boundaries in thin magnetic films

This paper discusses the effect of magnetic crystallographic anisotropy on the mobility of the domain walls in thin magnetic films with an easy axis in the plane of the film. It shows that the stable configuration of a domain wall is a single-vortex Bloch domain wall. Besides this, there are two metastable states of the domain wall—a Neel domain wall and a domain wall with two magnetic vortices along the normal to the plane of the film. It is also shown that the mobilities of the single-vortex and Neel domain walls and the domain wall with two vortices decrease as the anisotropy constant increases and tend to the same value.

Domain structure dynamics in ferromagnetic CrBr 3 studied by nuclear magnetic resonance

Nuclear magnetic resonance of 53Cr in ferromagnetic CrBr 3 in external magnetic fields was studied at 4.2 K. In zero field, a well-resolved NMR triplet (at 54.434 ± 0.297 MHz) was observed from domains, a single resonance (54.86 MHz) from domain walls, and a weak signal from Bloch lines (54.0 MHz). The NMR broadening, which is observed when the saturation field is achieved (3.08 kOe for the field parallel to the c 6-axis), is explained by the inhomogeneous penetration of the field into the sheet-formed crystal. The signal intensities at different RF polarizations indicate that the NMR enhancement coefficient is determined by the rotation of domain magnetization in the case of domains, and by the oscillatory motion of Bloch lines in the case of Bloch lines and domain walls. The ferromagnetic system does not shield the nuclei from the external magnetic field applied perpendicular to the c 6-axis. Such a field removes the NMR degeneracy in domain walls, thus forming a broad absorption band with distinct maxima. This band cannot be explained only in terms of the external field and the induced dipolar fields. The Cr +3 magnetization is assumed to depend, besides on orientation, on static gradients, which may be due to the spin-wave excitation and zero oscillations of domain walls and Bloch lines.

Three-dimensional simulation of the disturbance of magnetic domain walls by magnetic force microscope tips

The micromagnetics of the interaction of a strong 3D magnetic force microscope tip with a 180° asymmetric Bloch domain wall in an 80 nm {100} iron film has been simulated numerically using cubic elements on a 3D lattice. The distortion of the wall is found to be quite well localized on the scale of the tip dimensions, 60×60 nm2. The force of attraction between tip and film and the changes in self-energy of the wall and in the energy of the tip-sample system have been calculated for various positions of the tip. The strong attraction between tip and sample is slightly reduced (∼5%) when the tip is directly over the central vortex in the wall.

A route to chaos in a one-dimensional ferromagnet containing Bloch domain wall

The model of a uniaxial one-dimensional ferromagnet containing a single 180° Bloch domain wall is investigated by a numerical solution of the ac driven Landau-Lifshitz equation. A variety of possible motion of the magnetization vector — periodic, quasi-periodic, and chaotic — has been found in dependence on its space location and the amplitude of the drive field. The correlation dimension is also calculated for data taken at different locations of two qualitatively different chaotic attractors.

Spatial intermittency in a magnetic system with solitons

Spatial correlations in chaotic states of the Bloch domain wall of a uniaxial thin film are studied by means of a nonlinear correlation coefficient. A spatial intermittency in which regions of different chaotic dynamics are interlaced is discussed.

Current-induced displacements of Bloch walls in Ni-Fe films of thickness 120–740 nm

Rectangular current pulses of duration 0.14 μs, flowing across Bloch domain walls in Ni81Fe19 films, cause displacements Δx of these walls, observable by Kerr-contrast microscopy. In zero magnetic field, Δx reaches ≂14 μm/pulse at current densities ≂30% above the value jc where wall motion starts. This critical current density is jc≂1.2×1010 A/m2 for a film thickness w=263 nm. We have measured jc versus film thickness for w=120–740 nm, and find jc∝w−2.1. This suggests strongly that the observed wall motion is associated with an S-shaped distortion of the wall by the circumferential magnetic field of the current. This wall distortion is limited by the wall surface tension. The wall structure becomes that of the so-called asymmetric Néel wall. Through wall distortion, the current pulse pumps kinetic energy and momentum into the wall. This kinetic energy is then dissipated during ballistic wall motion happening largely after the end of the pulse. We also find jc to be independent of pulse duration.

Magnetic force microscopy of single crystal magnetite (Fe3O4)(abstract)

The micromagnetic domain structure of a magnetite (Fe3O4) single crystal has been studied using a magnetic force microscope (MFM). The MFM responds to the perpendicular component of the stray field above the magnetite surface. The sample was polished in the (011) plane. In this case, there are two easy magnetic axes parallel to the surface. Surface domains observed near cracks and edges have a complex closure structure (see Fig. 1), while walls seen far from such boundaries have a sinusoidal structure. Of particular interest is the presence of walls with either even or odd symmetry of the perpendicular stray field component across the transition. These can be conventionally modeled as Bloch or Neel walls, respectively. Both types of walls have been modeled and compared with the experimentally observed structures. We find the Bloch domain walls to be about 300 nm wide, nearly twice the value expected from bulk wall calculations. This distinction is consistent with a surface broadening of the domain wall due to magnetostatic effects.